Edge-Detection in Signals using the Continuous Wavelet-Transform.: Edge-Detection in Medical UltraSound Images.

Today, UltraSound (US) images are often used in medical examination and surgery. An improvement of the quality of these US-images will lead to many advantages, which is a big motivation for research on this field. One obstacle in improving the quality of the images is the presence of noise and texture. In order to distinguish this unwanted information from the interesting objects, different techniques can be used. Characteristic features, such as the ability to find vague contours, small objects or edges of small strength, decides if the technique is suitable for analysing noisy signals. This thesis presents different techniques for finding objects in US-images by using the continuous wavelet-transform. One observation from the analysis is that for edge-detectors using the wavelet-transform at a single scale, there is a compromise between accuracy and reliability. One has to choose between detecting small objects or vague contours. At fine scales one is able to detect small objects, but not objects with a vague contour without including redundant information. At coarse scales one is able to detect vague contours without including redundant information, but one will not detect small objects. The Lipschitz-regularity and the length of a maxima-line in the time-scale plane works well to find the points where the signal changes with a long duration, but is less suitable to find small objects and to remove unwanted information. By using the value of the wavelet-transform at several scales, it is possible to find vague contours in images, small objects, and edges of small strength compared to the strength of the noise. Another important observation from the analysis is that use of the circumference of objects is appropriate in order to find the most important objects in an image. Using this information has been very useful with respect to the analysis of US-images. Medical ultra-sound images are in general of varying quality. In addition the quality of a US-image will typically change within the signal, and changes with respect to the quality of the contour of objects and the influence of noise. The technique which in general is most reliable and produces the best representations of the US-images analysed in this thesis, uses information about the amplitude of the wavelet-transform both within and across scales, in addition to information about the circumference of the objects. This combined edge-detector is reliable with respect to represent the important objects in the image, and this representation is often easily obtained by the edge-detector